Which of the following systems are inconsistent? (a) x + 2y + z = 2 (b)...
3. Use Cramer's rule to solve the following equation systems: (a) 8x1 - x2 = 16 (©) 4x + 3y - 2z=1 2x2 + 5x3 = 5 x + 2y = 6 2X1 + 3x3 = 7 3x + Z=4 (6) - X1 + 3x2 + 2x3 = 24 (d) -x + y +7= a X, + x3 = 6 x-y+z=b Sx2 - X+Y-7=C X3 = 8
B C and E
LV VIJ Lou Loui 2. Solve each of the following linear systems using Gaussian Elimination and give a representation of each solution set: a. 2x - y = -3 x+3y = 0 3 - 2y + 2 b. 2x - 4y 2+2 = = = 1 -2 0 4.0 - 2y + 2z c. 2x + 5y + z -2.0 + y - 2 = = = -3 1 2 d 2x1 + 3x2 - 23...
Suppose we are looking for the point on the plane x + 2y + z = 5 closest to the point (2,3,0). Which of the following approaches DOES NOT lead to the answer? = 0 Solve the system of equationsJ 2(x - 2) - 2(5 - x - 2y) | 2(y-3) - 4(5 - x - 2y) = 0 Find the intersection point of the line r(t) = (2+ t, 3 + 2t, t) with the given plane. 2(x 2...
3. Solve the following systems of equations using Gaussian elimination. (a) 2x 3x2 + 2x3 = 0 (d) 2x + 4x2 2.xz 4 *- x2 + x3 = 7 X; - 2x2 · 4x3 = -1 -X, + 5x2 + 4x3 = 4 - 2x - X2 3x3 = -4
2. Follow the steps to verify the Divergence Theorem forF(x, y, z)-(z2, 2y, 49) and the solid cylinder E : r2 + y2 < 4, 0 2. (a) 9 pts] Evaluate F dS directly where S is the closed cylinder S which bounds E oriented outward. Note that S consists of three surfaces: S1 the surface of the cylinder x2 + y-4 for 0 z 2, the disc Di : x2 +92-4 which lies in the plane z 0 and...
2. Solve the following linear systems of equations by writing the system as a matrix equation Ax = b and using the inverse of the matrix A. (You may use a calculator or computer software to find A-1. Or you can find A-1 by row-reduction.) 3x1 – 2x2 + 4x3 = 1 x1 + x2 – 2x3 = 3 2x1 + x2 + x3 = 8 321 – 2x2 + 4x3 = 10 X1 + x2 – 2x3 = 30...
Which of the following are linear transformations? f: R3 R2 [x, y, z] [7x - 2y, 0 h R R x > sin x g R2R [x, y] [y- x, 2 the map T R > R< described by reflection in a line L: 2x + 7y = 0 through the origin.
10r y Which ofthe flywing is equivalent 1T77 ? 2x A. 9. B. 2y 2x 3r -9x + 18 10 Which of the following is equivalent to the fraction 6-x x2-25 When is divided by , the quotient is x +5 9x A. 27x B. 3r-15 x-20 C. 12. Which ofthe following is equivalent to-li A. B.一 D. 13. Which equation represents a line that is perpendicular to the line represented by 2x-y 77 B. y=-x+6 C. y=-2x + 6...
Use the Gaussian elimination method to solve each of the following systems of linear equations. In each case, indicate whether the system is consistent or inconsistent. Give the complete solution set, and if the solution set is infinite, specify three particular solutions. 1-5x1 – 2x2 + 2x3 = 14 *(a) 3x1 + x2 – x3 = -8 2x1 + 2x2 – x3 = -3 3x1 – 3x2 – 2x3 = (b) -6x1 + 4x2 + 3x3 = -38 1-2x1 +...
4. (25 points) Which of the following subsets of R3 are subspaces.Explain. a) {(x, y, z) 1 x 0, y 0, z ? c) {(z, y, z) | x2 + y2 + z2-1} d) Is the set H of all matrices of the form |(a,0)T, (b,d)T] a subspace of the space of all 2x2 matrices with the usual matrix addition and scalar multiplica- tion?